Question 5
SurdsGiven that p = 1 + √2 and q = 1 − √2, evaluate (p2 − q2)/2pq
- A.−2(2 + √2)
- B.2(2 + √2)
- C.−2√2
- D.2√2
Show the answer and explanation
Answer: C (−2√2)
Explanation
p2 − q2 = (p + q)(p − q) = 2 × 2√2 = 4√2, and pq = 1 − 2 = −1, so 2pq = −2. The value is 4√2 ÷ (−2) = −2√2.